{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning a Potential\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/optim/Learn_Potential.ipynb)\n",
    "\n",
    "In this example, we train a neural network to approxiamte a potential function $\\phi(x,y)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install --quiet phiflow\n",
    "from phi.torch.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well.\n",
    "from tqdm.notebook import trange"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We begin by defining and sampling the function $\\phi(x,y) = \\cos(\\sqrt(x^2+y^2))$ we want to learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def potential(pos):\n",
    "    return math.cos(math.vec_length(pos))\n",
    "\n",
    "landscape = CenteredGrid(potential, x=100, y=100, bounds=Box(x=(-5, 5), y=(-5, 5)))\n",
    "plot(landscape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we create a fully-connected network with three hidden layers and an Adam optimizer.\n",
    "We use a standard $L^2$ loss function (MSE loss) and use all sample points from the above grid as training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[92m(xᵇ=100, yᵇ=100)\u001b[0m \u001b[94m0.238 ± 0.192\u001b[0m \u001b[37m(1e-09...6e-01)\u001b[0m"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.seed(0)\n",
    "net = dense_net(2, 1, [32, 64, 32])\n",
    "optimizer = adam(net)\n",
    "\n",
    "def loss_function(x, label):\n",
    "  prediction = math.native_call(net, x)\n",
    "  return math.l2_loss(prediction - label), prediction\n",
    "\n",
    "input_data = rename_dims(landscape.points, spatial, batch)\n",
    "labels = rename_dims(landscape.values, spatial, batch)\n",
    "loss_function(input_data, labels)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's train the network for 200 iterations!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 288x216 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 288x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "loss_trj = []\n",
    "pred_trj = []\n",
    "for i in range(200):\n",
    "  loss, pred = update_weights(net, optimizer, loss_function, input_data, labels)\n",
    "  loss_trj.append(loss)\n",
    "  pred_trj.append(pred)\n",
    "loss_trj = stack(loss_trj, spatial('iteration'))\n",
    "pred_trj = stack(pred_trj, batch('iteration'))\n",
    "plot(math.mean(loss_trj, 'x,y'), err=math.std(loss_trj, 'x,y'), size=(4, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now visualize how the prediction changes during training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "NzcuMTAw\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x1d48db45400>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_grid = rename_dims(pred_trj.iteration[::4], 'x,y', spatial)\n",
    "plot(pred_grid, animate='iteration', size=(6, 5))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "phiflow2",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
